Let us also briefly mention that this conjecture has a birational version,
proved for projective hyperkähler manifolds by E. Markman in
[1]} and generalized in [2]} to the non-projective case. In this birational
version, the nef cone is replaced by the birational nef cone (that is, the
closure of the union of pullbacks of Kähler cones on birational models of \(M\) )
and the group \(\operatorname{Aut}(M)\)  is replaced by the group of birational automorphisms \(\operatorname{Bir}(M)\) .
